Dotnet - flatten a tree (list of lists) with one statement?

Question

Hi,

Thanks to nHibernate, some of the data structures I work with are lists within lists within lists. So for example I have a data object called "category" which has a .Children property that resolves to a list of categories ... each one of which can have children ... and so on and so on.

I need to find a way of starting at a top-level category in this structure and getting a list or array or something similar of all the children in the entire structure - so all the children of all the children etc etc, flattened into a single list.

I'm sure it can be done with recursion, but I find recursive login a pain to work through, and I'm convinced there must be a more straightforward way in .net 4 using Linq or somesuch - any suggestions?

Cheers, Matt

Answer 1

Assuming your Category class looks something like:

 public class Category
 {
   public string Name { get; set; }
   public List<Category> Children { get; set; }
 }

I don't think there's an "easy" non-recursive way to do it; if you're simply looking for a single method call to handle it, the "easy" way is to write the recursive version into a single method call. There's probably an iterative way to do this, but I'm guessing it's actually pretty complicated. It's like asking the "easy" way to find a tangent to a curve without using calculus.

Anyway, this would probably do it:

public static List<Category> Flatten(Category root) {

    var flattened = new List<Category> {root};

    var children = root.Children;

    if(children != null)
    {
        foreach (var child in children)
        {
            flattened.AddRange(Flatten(child));
        }
    }

    return flattened;
}

Answer 2

Here's an extension method that does the job:

// Depth-first traversal, recursive
public static IEnumerable<T> Flatten<T>(this IEnumerable<T> source, Func<T, IEnumerable<T>> childrenSelector)
{
    foreach (var item in source)
    {
        yield return item;
        foreach (var child in childrenSelector(item).Flatten(childrenSelector))
        {
            yield return child;
        }
    }
}

You can use it like this:

foreach(var category in categories.Flatten(c => c.Children))
{
    ...
}

The solution above does a depth-first traversal, if you want a breadth-first traversal you can do something like this:

// Breadth-first traversal, non-recursive
public static IEnumerable<T> Flatten2<T>(this IEnumerable<T> source, Func<T, IEnumerable<T>> childrenSelector)
{
    var queue = new Queue<T>(source);
    while (queue.Count > 0)
    {
        var item = queue.Dequeue();
        yield return item;
        foreach (var child in childrenSelector(item))
        {
            queue.Enqueue(child);
        }
    }
}

It also has the benefit of being non-recursive...

---

UPDATE: Actually, I just thought of a way to make the depth-first traversal non-recursive... here it is:

// Depth-first traversal, non-recursive
public static IEnumerable<T> Flatten3<T>(this IEnumerable<T> source, Func<T, IEnumerable<T>> childrenSelector)
{
    LinkedList<T> list = new LinkedList<T>(source);
    while (list.Count > 0)
    {
        var item = list.First.Value;
        yield return item;
        list.RemoveFirst();
        var node = list.First;
        foreach (var child in childrenSelector(item))
        {
            if (node != null)
                list.AddBefore(node, child);
            else
                list.AddLast(child);
        }
    }
}

I'm using a LinkedList<T> because insertions are O(1) operations, whereas insertions to a List<T> are O(n).